Question

answer the q in the pic below

Answer 1

Diagonals in pentagon are C(5,2)- 5= 5
Hexagon C(6,2)-6 =9
Octagon C(8,2) =20
Polygon C(n,2)-n

Answer 2

$b) \blue { If \: number \:of \:sides \:of \:a }\\\blue {polygon } \pink {= n}$

$then \:\blue { number \: of \: diagonals}\pink { = \frac{n(n-3)}{2}}$

$a_{1}) Number \:of \: sides \:in \: pentagon (n)=5$

$Number \: diagonals = \frac{5(5-3)}{2} \\=\frac{5 \times 2 }{2} = 5$

$a_{2}) Number \:of \: sides \:in \: Hexagon (n)=6$

$Number \: diagonals = \frac{6(6-3)}{2} \\=\frac{6 \times 3 }{2} = 9$

$a_{3}) Number \:of \: sides \:in \: Heptagon (n)=7$

$Number \: diagonals = \frac{7(7-3)}{2} \\=\frac{7 \times 4 }{2} = 14$

$a_{4}) Number \:of \: sides \:in \: Octagon (n)=8$

$Number \: diagonals = \frac{8(8-3)}{2} \\=\frac{8 \times 5 }{2} = 20$

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